The Ideal Gas Law

The ideal gas law combines Boyle's Law, Charles's Law, and Avogadro's Law into a single equation that describes the state of an ideal gas — one in which molecules have no volume and no intermolecular forces.

The Equation

$PV = nRT$

Where:

• $P$ is the pressure (Pa = N/m²)
• $V$ is the volume (m³)
• $n$ is the amount of gas (mol)
• $R = 8.314\,\text{J/(mol·K)}$ is the universal gas constant
• $T$ is the absolute temperature (K)

Three Rearrangements

Solving for each variable:

$P = \frac{nRT}{V}$

$V = \frac{nRT}{P}$

$T = \frac{PV}{nR}$

Standard Conditions

At standard temperature and pressure (STP: $T = 273.15\,\text{K}$, $P = 101325\,\text{Pa}$), one mole of an ideal gas occupies approximately $22.4\,\text{L} = 0.0224\,\text{m}^3$.

This is the molar volume of an ideal gas at STP, a useful benchmark for checking calculations.

Limits of the Ideal Gas Model

Real gases deviate from ideal behavior at:

• High pressure — molecules are compressed close enough that their volume matters
• Low temperature — intermolecular attractions become significant

The van der Waals equation corrects for these effects:

$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$

Where $a$ accounts for intermolecular attractions and $b$ accounts for molecular volume. For most introductory problems, the ideal gas law is an excellent approximation.

Your Task

Implement the three functions below using $R = 8.314\,\text{J/(mol·K)}$.